Structural transformations in nanomaterials
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Structural transformations in nanomaterials

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Structural transformations in nanomaterials Structural transformations in nanomaterials Presentation Transcript

  • Structural transformations in nanomaterials Deepak Varandani
  • Nanomaterials
    • Materials with structural elements which have at least one dimension less than 100 nm
    • Polycrystals with finest grains and extremely high fraction of boundaries
    • Quantum confinement of charge carriers
    • Larger fraction of surface atoms
      • Lead to significantly altered properties
    Characteristic features Definition
  • Boundary/Interface volume fraction d= 5 nm V.F.= 50 % d= 12 nm V.F.= 50 % d Δ
  • Structure of boundaries
    • Adjacent misoriented crystallites separated by grain boundaries
    • Boundaries carry the crystallite geometric mismatch
      • Dislocations, Vacancies
    • Coarse grained polycrystals
    • Volume fraction extremely low (<1%)
    • Low angle, high angle, non-equilibrium, amorphous
  • Structure of…..
    • Nanocrystals
    • Volume fraction high. Triple junctions important
    • Conflicting reports
      • Long-range stresses, frozen-gas like behaviour, reduced density, high energy
      • Well ordered, low energy, small excess volumes
        • Structure mostly non-equilibrium
    • Boundary structure crucially depends on synthesis conditions
    • Affects the structure of the crystallites they surround
  • Structural transformations
    • Solids exist in different structural phases depending on temperature, pressure and other ambient conditions
    • In nanomaterials size is an additional variable controlling structure
    amorphization Nanomaterials allotropic transformations lattice distortion metastable phases crystallites/grains
  • Lattice distortion The variation in Pd (111) peak with the nanoparticle size, showing the size induced lattice contraction Variation of Debye Waller parameter with grain size in Se
      • Unit cell dimensions
      • Debye-Waller parameter
      • Debye temperature
    Pd nanoparticle layers Se nanoparticle layers Zhang 1997 Aruna 2005
      • Lattice expansion or contraction
  • Metastable phase stabilization Normalized unit cell volume (N.U.C.V.) as a function of particle size for different phases of Al 2 O 3 Mole percentage of tetragonal phase in BaTiO 3 as a function average particle size Lattice expansion along with structural transformation in Al 2 O 3 nanoparticles Cubic metastable phase in BaTiO 3 Kwon 2006 Ayyub 1995
  • Theoretical considerations
    • Interface driven structural transformations
      • Nanocrystallites enveloped by highly non-equilibrium grain boundaries
        • reduced density or excess volume
        • vacancies, vacancy clusters, extrinsic dislocations
      • Defects generate stress fields
      • Atoms displaced from equilibrium positions due to stresses
  • Interface driven…..
    • Square shaped grains with orthogonal boundaries
    • Stress due to vacancy and vacancy clusters  x -3 , . x is the distance from the defect center
    a 0 = perfect lattice interatomic separation ξ = mean grain boundary width Δ V= excess grain boundary volume d=crystallite diameter
    • Lattice distortion depends on a 0 and microstructure
    • Distortion mainly in thin layer near boundary
    Qin 1992
  • Thermodynamic treatment
    • G=U-TS+PV…………….Volumetric free energy
    • G=U-TS+(P+ Δ P)V+ γ A …….. Size independent
    • γ A= Surface free energy
    U=internal energy T=temperature, P=pressure, V=volume, A=area Δ P=excess internal pressure due to surface stress γ =surface energy density
    • Free energy G decides which phase is stable
    • G is modified for small particles
    Gilbert 2003
  • Thermodynamic……
    • At small sizes metastable phases may have low total G due to low γ
    • Thus phase inversion at nanodimensions is possible
    Size-dependence of structure in Co nanoparticles Ram 2001 Structure Size Surface energy density (J/m 2 ) hcp (bulk stable) fcc (metastable) bcc (metastabe) 10-20 nm 2-5 nm 2.79 2.73 2.73
  • Thermodynamic ……..
    • Co nanoparticles
    • Thus lower surface energy ensures that below a critical size fcc or bcc phase is stabilized in preference to hcp phase
    Sample Lattice parameters (nm) Lattice area (10 −2 nm 2 ) Lattice volume (10 −3 nm 3 ) Lattice surface energy (10 −20 J) Bulk hcp structure fcc structure a=0.2507 c=0.4070 a= 0.3545 93.90 75.40 66.50 44.55 261.98 205.85 bcc structure fcc structure a =0.2840 a=0.3540 48.39 75.19 22.91 44.36 132.11 205.27 fcc structure a=0.3535 74.98 44.17 204.70
  • Amorphization
    • G c <G A +G D
    • G c =Free energy of crystalline phase
    • G A =Free energy of amorphous phase
    • G D =energy increase due to defects
    • In nanomaterials the anti-site disorder & anti-phase boundaries increase G d , resulting in amorphization
  • Universal thermodynamic approach
    • P l -P o =2 γ /r
    P l =pressure inside P o =pressure outside γ =surface tension/energy r=radius
    • As size decreases metastable phase region is driven into its strongly unstable region due to the shift in the phase boundary line
    • In fine particles internal pressure increases due to Laplace-Young effect
    Wang 2005 P(r,T)=a+bT-2 γ /r
  • Bond-OLS correlation mechanism
    • Atoms at surface suffer bond order loss
    • Spontaneous relaxation of rest of bonds: Contraction or expansion
    • Reduced binding energy and increase in bond strength
    • In nanomaterials effect is significant
    c i = contraction (<1) or expansion (>1) factor for the ith layer (i≤3) b i , E B (b i ) are respectively the bond length and the binding energy of the ith atomic layer of atoms b, E B (b) are respectively the bond length and the binding energy of the bulk atoms z i = coordination number of the ith layer m = a parameter which varies with the nature of the bond, being equal to 1 for elemental solids and 4 for compounds and alloys. Sun 2002
  • Bond-OLS …….. Δ b= lattice distortion  i = N i /N= weighting factor The bond-OLS correlation mechanism as applied to the case of lattice contraction in Ni, Cu and Ag. Agreement is reached by taking z 1 =4 (c 1 =0.88, 0.9), z 2 =6 (c 2 =0.96, 0.97) and m=1 (Sun 2002).
  • Conclusions
    • Boundary component critically influences structure
    • Boundary defects generate stress fields, leading to static distortion of lattice
    • Metastable phases stabilized below a critical crystallite size: Explained using free energy considerations
    • UTA and BOLS mechanism commonly invoked to explain structural transformations
    • Need to recognize the role of synthesis conditions
    • Size calculated using different techniques. Unambiguous comparison difficult
  • References
    • H. S. Kim, Y. Estrin and M. Bush, Acta Mater. 48 , 493 (2000)
    • I. Aruna, B. R. Mehta and L. K. Malhotra, Applied Physics Letters 87 , 103101 (2005)
    • Y. H. Zhao, K. Zhang, and K. Lu*, Phys. Rev. B 56 , 14322 (1997).
    • Pushan Ayub, V. R. Palkar, Soma Chattopadhyay and Manu Multani, Physical Review B 51 (9) , 6135 (1995)
    • Soon-Gyu Kwon, Kyoon Choi, Byung-Ik Kim, Materials Letters 60 , 979 (2006)
    • W. Qin, Z. H. Chen, P. Y. Huang and Y. H. Zhuang, Jl. Alloys and Comp. 292 , 230 (1999)
    • Benjamin Gilbert, Hengzhong Zhang, Feng Huang, Michael P. Finnegan, Glenn A. Waychunas and Jillian F. Banfield, Geochem. Trans. 4 , 20 (2003)
    • S. Ram, Materials Science and Engineering A 204-306 , 923 (2001)
    • C. X. Wang, G. W. Yang, Materials Science and Engineering R 49 , 157 (2005)
    • Chang Q Sun, B. K. Tay, X. T. Zeng, S. Li, T. P. chen, Ji Zhou, H. L. Bai and E. Y. Jiang, J. Phys. Condens. Matter 14 , 7781 (2002).